A video game costs \( \$ 60 \) today. If the inflation rate is \( 4.75 \% \) and is compounded continuously how much will this same video game cost in 5 years?

To calculate the future cost of the video game due to inflation, we can use the continuous compounding formula, which is given by: \[ A = Pe^{rt} \] Where: - \( A \) is the amount of money accumulated after time \( t \). - \( P \) is the principal amount (the initial cost of the game, which is \( \$60 \)). - \( e \) is the base of the natural logarithm (approximately \( 2.71828 \)). - \( r \) is the annual interest rate (inflation rate in this case, which is \( 0.0475 \)). - \( t \) is the time in years (which is \( 5 \)). Plugging in the values: \[ A = 60e^{0.0475 \times 5} \] First, calculate \( 0.0475 \times 5 \): \[ 0.0475 \times 5 = 0.2375 \] Now calculate \( e^{0.2375} \): \[ e^{0.2375} \approx 1.2684 \] (using a calculator or mathematical software) Now plug it back into the equation: \[ A \approx 60 \times 1.2684 \approx 76.11 \] So, the video game will cost approximately \( \$76.11 \) in 5 years when accounting for continuous inflation at a rate of \( 4.75\% \).